Chapter 4: Q 62 (page 387)

In the following exercise, solve the systems of equations by elimination.
$\{\begin{cases} x - 4 y = - 1 \\ - 3 x + 12 y = 3 \end{cases}$

Short Answer

Expert verified

The given system has infinitely many solutions.

Step by step solution

Step 1. Given information

The given linear equations are :

$x - 4 y = - 1 - 3 x + 12 y = 3$

Step 2. Calculating the value of y

To calculate the value of $y$ , we have to eliminate the $x$ term. For which we will do the following changes in the equation, so that $x$ term can be easily eliminated.

Multiply first equation by 3

$3 (x - 4 y = - 1) 3 x - 12 y = - 3$

now, the equations are

$3 x - 12 y = - 3 - 3 x + 12 y = 3$

now simply add the equations

$3 x - 12 y = - 3 - 3 x + 12 y = 3 0 = 0$

This means that the above equation is satisfied for all the values of $x$ and $y$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercise, solve the systems of equations by elimination.
$\{\begin{cases} x - 4 y = - 1 \\ - 3 x + 12 y = 3 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the value of y

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Statistics

Calculus

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercise, solve the systems of equations by elimination.x-4y=-1-3x+12y=3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the value of y

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Statistics

Calculus

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercise, solve the systems of equations by elimination.
$\{\begin{cases} x - 4 y = - 1 \\ - 3 x + 12 y = 3 \end{cases}$